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anonymous
 5 years ago
Find all the values of x in the interval [0, 2pie] that satisfy the equation 2cos(x) + sin(2x) = 0.
anonymous
 5 years ago
Find all the values of x in the interval [0, 2pie] that satisfy the equation 2cos(x) + sin(2x) = 0.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0step one is to rewrite \[sin(2x)=2sin(x)cos(x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then you get \[2cos(x)+2cos(x)sin(x)=0\] \[2cos(x)(1+sin(x))=0\] \[cos(x)=0\] or \[1+sin(x)=0\] \[sin(x)=\frac{1}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can you solve from there?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can you continue please?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sure. you are in the interval \[(0,2\pi)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in that interval cosine is 0 at \[\frac{\pi}{2}\] and \[\frac{3\pi}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you do not instantly know where \[sin(x)=\frac{1}{2}\] then look at the cheat sheet http://tutorial.math.lamar.edu/cheat_table.aspx and see that it is at \[\frac{7\pi}{6}\] and \[\frac{11\pi}{6}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that is where the second coordinate is \[\frac{1}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0unit circle on last page of cheat sheet
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